Geodesic
On the extremality of regular extensions of contents and measures
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 2, pp. 213-218 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $\Cal A$ be an algebra and $\Cal K$ a lattice of subsets of a set $X$. We show that every content on $\Cal A$ that can be approximated by $\Cal K$ in the sense of Marczewski has an extremal extension to a $\Cal K$-regular content on the algebra generated by $\Cal A$ and $\Cal K$. Under an additional assumption, we can also prove the existence of extremal regular measure extensions.
Let $\Cal A$ be an algebra and $\Cal K$ a lattice of subsets of a set $X$. We show that every content on $\Cal A$ that can be approximated by $\Cal K$ in the sense of Marczewski has an extremal extension to a $\Cal K$-regular content on the algebra generated by $\Cal A$ and $\Cal K$. Under an additional assumption, we can also prove the existence of extremal regular measure extensions.
Classification : 28A12, 46E27
Keywords: regular content; lattice; semicompact; sequentially dominated 
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     author = {Adamski, Wolfgang},
     title = {On the extremality of regular extensions of contents and measures},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {213--218},
     year = {1995},
     volume = {36},
     number = {2},
     mrnumber = {1357522},
     zbl = {0834.28001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1995_36_2_a0/}
}
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Adamski, Wolfgang. On the extremality of regular extensions of contents and measures. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 2, pp. 213-218. http://geodesic.mathdoc.fr/item/CMUC_1995_36_2_a0/